SIR must be evaluated in the receiver of WCDMA systems. A good estimate of SIR is needed mainly for fast power control and also for radio resource management. Implementation point of view is that the SIR estimation should be computationally as simple as possible since it has to be done every time slot for every radio link connection.
The estimation of SIR requires the estimation of signal power and of interference power. There are two main categories of methods to estimate SIR, namely one with wideband interference estimation and another with narrowband interference estimation. The wideband interference estimation is calculated from the wideband signal which is the signal before despreading. The narrowband interference estimation is calculated from the narrowband signal which is the signal after despreading. In the following, both methods are introduced shortly, by discribing one possible implementation of these methods (although there are further possible implementations which, however, are not mentioned here):
1. SIR Estimation with Wideband Interference Estimate:
The signal to interference ratio is described by the following equation:
                    SIR        =                                            SF              DPCCH                        ·            S                                              I              0                        +                          I              r                                                          (        1        )            where                S is the received signal power of a dedicated physical control channel (DPCCH),        SFDPCCH is the processing gain of the DPCCH channel,        Ir is the wideband interference originating from own cell,        I0 is the wideband interference from other cells including the system thermal noise.        
Equation (1) needs the estimation of the signal power and the interference power.
The signal power is calculated from despread pilot symbols separately for each antenna using the following equation:
                              S          ⋒                =                                            ∑                              k                =                1                            L                        ⁢                                          S                ⋒                            k                                =                                    ∑                              k                =                1                            L                        ⁢                                                                                                1                                          N                      p                                                        ⁢                                                            ∑                                              i                        =                        1                                                                    N                        p                                                              ⁢                                          z                                              k                        ,                        i                                                                                                                        2                                                          (        2        )            where                L is the number of allocated fingers for current antenna (number of received paths),        Np is the number of pilot symbols,        z is the sample of the DPCCH channel from which the pilot modulation is removed,        
Samples z are complex values and there are Np number of them. It has to be noted that the signal power estimate S is biased by the second term in the following equation:
                              E          ⁡                      (                          S              ⋒                        )                          =                  S          +                                                    (                                                      I                    0                                    +                                      I                    r                                                  )                            ·              L                                                      N                p                            ·                              SF                DPCCH                                                                        (        3        )            
The wideband power per antenna is calculated from the received signal by the following equation:
                                          P            ⋒                    w                =                              1            N                    ⁢                                    ∑                              i                =                1                            N                        ⁢                                                                            r                  i                                                            2                                                          (        4        )            where                N is the number of samples in one time slot,        r is the sample of the received signal after a pulse shape filter and AGC on current antenna.        
The interference for equation (1) is obtained from wideband power measurement using the following equation:E({circumflex over (P)})=S+I0+Ir  (5)
So, the SIR estimate for one antenna is calculated by the following equation:
                              S          ⁢                      I            ⋒                    ⁢          R                =                              SF            DPCCH                    ·                                                    S                ⋒                            -                                                L                                                            N                      p                                        ·                                          SF                      DPCCH                                                                      ·                                                      P                    ⋒                                    w                                                                                                      P                  ⋒                                w                            -                              S                ⋒                                                                        (        6        )            where all the symbols are as defined above.
The final SIR estimate is the sum of all antennawise estimates SÎR from equation (6).
The SIR estimation with wideband interference estimate is computationally not very complex. Complexity of wideband interference estimation increases directly proportional only to the number of receiver antennas. Only one value Pw per antenna is to be calculated and can be used for every connection (code channel) and every multipath. So, this method allows a simple implementation. A further advantage of this method is that only a small variance occurs.
However, a major drawback of this method is the biasing on very high bit rates, making it almost useless with high bit rates signal connections (approaching 2 Mb/s). The orthogonal share of the signal power should be removed from the wideband noise, but in real case neither the power ratio nor the orthogonality coefficient are unfortunately known. Because the orthogonal data channel power is not removed, in the equation (6), the numerator remains too small and the denominator too big. Thus SIR estimate remains too small, and the error grows with high SIR values and high bit rates. With high SIR values, noise power becomes small and unremoved share of the signal power starts to play an important role in wideband noise estimate. With high bit rates, power ratio becomes very small. Thus, the Unremoved share of the signal power becomes remarkable.
2. SIR Estimation with Narrowband Interference Estimate:
The signal to interference ratio is described by the following equation:
                    SIR        =                  S          I                                    (        7        )            where                S is the received signal power of a DPCCH channel,        I is the interference power including the system thermal noise (measured from the narrowband signal).        
Here again, equation (7) needs the estimation of the signal power and the interference power.
The signal power is calculated according to the above equation (2). It has to be noted that the signal power estimate Ŝ is biased. The bias can be removed after the antennawise noise and interference power is estimated. The unbiased signal power estimate is
                                          S            ⋒                    ub                =                                            ∑                              k                =                1                            L                        ⁢                                                                                                1                                          N                      p                                                        ⁢                                                            ∑                                              i                        =                        1                                                                    N                        p                                                              ⁢                                          z                                              k                        ,                        i                                                                                                                        2                                -                                    (                                                L                  ·                  I                                                  N                  p                                            )                        .                                              (        8        )            
In the minimum variance unbiased (MVU) estimation method, the noise and interference power is estimated from the narrowband received, despread and demodulated signal zk,i. The rationale behind this is as follows: Under the assumption that the power of the transmitted narrowband signal and the channel power stay constant for the calculation period (one timeslot) the variance of the received signal is actually equal to the variance of the noise and interference. For additive white Gaussian noise (AWGN) and interference, this in turn equals to the power of the noise and the interference.
It must be noted that here two assumptions have been made, one about the transmitted signal power, and another about the channel power. Since the transmit power control (TPC) period is one timeslot, the first assumption is right; the transmitted signal power stays constant over the calculation period. The validity of the second assumption depends on the channel, and the biggest error from the ideal situation would be for a fading channel with a very high Doppler frequency, so that the channel power changes significantly over one timeslot.
By definition variance is{circumflex over (σ)}{circumflex over (σ2)}=E(|X−E(X)|2),  (9)but it can be also calculated by{circumflex over (σ)}{circumflex over (σ2)}=E(|X|2) −|E(X)|2),  (10)|E(X)|2 has already been calculated in the above equation (2) since the term E(|X|2) corresponds to
                                          1                          N              p                                ·                                    ∑                              i                =                1                                            N                p                                      ⁢                                          z                                  k                  ,                  i                                            ·                              z                                  k                  ,                  i                                *                                                    ,                            (        11        )            where zk,i* is the complex conjugate of the despread and demodulated pilot symbol.
The estimate of the interference and noise power of finger k can be now written by substituting equation (11) and
      term    ⁢                  ⁢                  S        ^            k        =                                    1                      N            p                          ⁢                              ∑                          i              =              1                                      N              p                                ⁢                      Z                          k              ,              i                                                  2  from equation (8) to equation (10)
                                          I            ⋒                    k                =                              (                                          1                                  N                  p                                            ·                                                ∑                                      i                    =                    1                                                        N                    p                                                  ⁢                                                      z                                          k                      ,                      i                                                        ·                                      z                                          k                      ,                      i                                        *                                                                        )                    -                                    S              ⋒                        k                                              (        12        )            
To reduce the variance of the interference and noise power estimate
                              I          ⋒                =                              1            L                    ·                                    ∑                              k                =                1                            L                        ⁢                                                  ⁢                                          I                ⋒                            k                                                          (        13        )            of a current antenna, it is filtered using a 1-tap IIR filter with effective length of 4 timeslots, resulting in the following equation:Îfilt(t)=κ·Î(t)+(1−κ)·Î(t−1)  (14)
Here time index t refers to a current timeslot and (t−1) to a previous timeslot (mark fit Îfilt=Îfilt(t) The Kalman gain κ of the filter should be 0.25.
So, the SIR estimate for one antenna is calculated by the following equation
                                          SIR            ⋒                    =                                                                      S                  ⋒                                ub                                                              I                  ⋒                                filt                                      =                                                                                ∑                                          k                      =                      1                                        L                                    ⁢                                                                          ⁢                                                            S                      ⋒                                        k                                                  -                                  (                                      L                    ·                                                                                            I                          ⋒                                                filt                                            /                                              N                        p                                                                              )                                                                              I                  ⋒                                filt                                                    ,                            (        15        )            where all the symbols are as defined above.
The final SIR estimate is sum of all antennawise estimates SIR from equation (15).
The narrowband interference based SIR estimation doesn't have any biasing problems described above in conjunction with the wideband interference estimate.
However, it is computationally more complex than the above mentioned wideband interference method. Complexity of interference estimate increases directly proportional to the number of receiver antennas, number of connections (code channel), number of received paths per connection (different delays) and number of pilot bits. A further drawback is that the narrowband interference estimate has a high variance so that a high effort filtering is required which takes a certain time, but filtering causes error in case of a very fast fluctuation of the interference level; the latter case would be for exemple the presence of an other user in the same cell with a package data connection (CPCH).